Fourier series how can it be solved?

I really can't understand how fourier series works.. Like I tried solving problems..but till now, it didn't sink in my brain..
I just want 2 know the basic way of solving a problem regarding fourier series..then it will be much easier to understand I guess..
Thanx in advance..

Staff: Mentor

I really can't understand how fourier series works.. Like I tried solving problems..but till now, it didn't sink in my brain..
I just want 2 know the basic way of solving a problem regarding fourier series..then it will be much easier to understand I guess..
Thanx in advance..

What's the function that you want to find the Fourier series for? sin (n*pi) = 0 for all integers, as you point out, but it's otherwise not very interesting. Is the function f(x) = 0?
If so, all of the coefficients in the Fourier series would be 0.

What's the function that you want to find the Fourier series for? sin (n*pi) = 0 for all integers, as you point out, but it's otherwise not very interesting. Is the function f(x) = 0?
If so, all of the coefficients in the Fourier series would be 0.

Is there more to this problem that you haven't shown us?

hi mark
sorry 4 being late..plus giving a completely wrong question..
ok..
the I realize the problem is for example :
f(x)= sinx
0<x<pi
it's a problem I want to understand like how is it really solved?

A Fourier series for a function f(x) is an infinite sum such that
[tex]f(x)= \sum_{m=0}^\infty A_n cos(nx)+ B_n sin(nx)[/tex] (or other (x/L) or whatever inside the trig functions).

Of course, the right side of that is periodic with period [itex]2\pi[/itex] so if f is not itself periodic, that can only be true on some interval (which is one reason why you might need that "/L" to alter the interval).

But if f(x)= sin(x) is not only periodic with period [itex]2\pi[/itex], it is already of that form and it is obvious that [itex]A_n= 0[/itex] for all n, while [itex]B_1= 1[/itex] and [itex]B_n= 0[/itex] for all n greater than 1.

A Fourier series for a function f(x) is an infinite sum such that
[tex]f(x)= \sum_{m=0}^\infty A_n cos(nx)+ B_n sin(nx)[/tex] (or other (x/L) or whatever inside the trig functions).

Of course, the right side of that is periodic with period [itex]2\pi[/itex] so if f is not itself periodic, that can only be true on some interval (which is one reason why you might need that "/L" to alter the interval).

But if f(x)= sin(x) is not only periodic with period [itex]2\pi[/itex], it is already of that form and it is obvious that [itex]A_n= 0[/itex] for all n, while [itex]B_1= 1[/itex] and [itex]B_n= 0[/itex] for all n greater than 1.